If you want to help your body burn fat, then you have to put on more muscle. Yes you have to watch your calorie intake, but more muscle that you have, will raise your metabolism. You can build muscle 3 different ways. First you can build some without weights, build more with a light workout with weights, or go full out and build the most that your genes will allow, training with a lot of weight and training often.
You do not need weights to gain muscle. First off if you are a sedimentary type person, you just need to get up and get moving to improve your muscle tone. You can start walking at a pace that will raise your heart rate and make you break a sweat.
As you start toning and building some muscle you will find that the pace that once made you tired, will no longer do that. You will need to raise the pace to continue toning and adding more muscle.